Basic Information

It might be the result a Time Travel equivalent of the Prime Directive, in which case great pains are taken to make sure that nothing anachronistic is brought back. You wouldn't want a misplaced Grays Sports Almanac upsetting the timeline, would you?

Alternately, it's a function of how the Time Machine itself works. In this scenario, you're probably going to arrive naked.

Sources

Game and Story Use

The second version, famous for it's use in The Terminator, could be applied as an entertaining drawback to other technology or magic.

Teleportation is an obvious choice. "The good news is, upon reading the scroll you are instantly teleported back to the Palace. The bad news is, your treasure doesn't go with you. The really bad news is, you're also naked."

Levitation, Psychokinesis, Summoning spells, Flight, etc. Perhaps magic only resonates in living cells. A given magic might be able to fly 2000 lbs of human, but only 5 lbs of cloth or metal, and then only if supported on a human frame.

Could be that magic (in general) only works if the caster is Skyclad. Suddenly magic is a thing you only do in public if you've exhausted all other options.

A cursed gateway. This Portal to the Past dumps you out naked. While the locals of the past haven't figured out time-travel yet, they have lots of folklore concerning crazy naked people who show up in that particular neck of the woods. When the PCs arrive, they're ready for them.

This Time Machine has an over zealous Paradox Prevention Chip in it's AI. It won't send any technology back before the date it was invented. It may even refuse to send anyone back in time before they were born. Depending on the rest of it's personality, it may just refuse, or it may send you (or your stuff) to the wrong time.

The PCs are about invent time travel, when suddenly the Time Police show up. They explain that yes, you are about to make your prototype time machine work, however, before they'll allow you to enter another era, you must do a few things. There's waivers to be signed, and you need to initial here that your rights and responsibilities were explained to you. If you're planning on going back to the past, you'll first have to pass this quiz on the era. If you're not fluent in the language of that time, we won't let you go. Don't even think about bringing any technology into the past, either. We'll be monitoring your trip from our bunker in the future. Break these laws, and you'll be coming home on The Slow Path.